论文标题
一类带有状态延迟的切换线性系统的指数稳定性的稳健性
Robustness of Exponential Stability of a Class of Switched Linear Systems with State Delays
论文作者
论文摘要
本文研究了在任意切换下由线性功能微分方程描述的一类切换系统的指数稳定性的鲁棒性。我们将通过引入结构化稳定性半径的概念来衡量这种系统的稳定性，但要受其组成子系统矩阵的参数仿射扰动。在某些相关的正线性系统上限上给定子系统具有通用的线性共阳性lyapunov函数的假设下，建立了此半径的下限和上限。在具有离散多个延迟或分布式延迟的切换正线性系统的情况下，获得的结果为稳定性半径带来了一些可易于计算的界限。给出了示例以说明所提出的方法。
This paper investigates the robustness of exponential stability of a class of switched systems described by linear functional differential equations under arbitrary switching. We will measure the stability robustness of such a system, subject to parameter affine perturbations of its constituent subsystems matrices, by introducing the notion of structured stability radius. The lower bounds and the upper bounds for this radius are established under the assumption that certain associated positive linear systems upper bounding the given subsystems have a common linear copositive Lyapunov function. In the case of switched positive linear systems with discrete multiple delays or distributed delay the obtained results yield some tractably computable bounds for the stability radius. Examples are given to illustrate the proposed method.
